Multifractals competing with solitons on Fibonacci optical lattices
Multifractals competing with solitons on Fibonacci optical lattices
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DOI：
10.1088/1367-2630/14/11/113012
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发表时间：
2011-10
影响因子：
3.3
通讯作者：
M. Takahashi;H. Katsura;M. Kohmoto;T. Koma
中科院分区：
文献类型：
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作者：
M. Takahashi;H. Katsura;M. Kohmoto;T. Koma
我们研究了Fibonacci晶格上非线性薛定谔方程的定态，这有望通过加载到光学晶格中的玻色-爱因斯坦凝聚来实现。当模型中没有非线性项时，波函数和谱都具有分形结构。这种波函数被称为临界波函数。我们提出了一个相图的能量谱变化的非线性。它由三部分组成：禁带、临界态谱和定态孤子谱。我们发现，临界态的能谱保持完整，而不考虑大量的定态孤子的非线性。
We study stationary states for the nonlinear Schrödinger equation on Fibonacci lattices, which are expected to be realized by Bose–Einstein condensates loaded into an optical lattice. When the model does not have a nonlinear term, the wavefunctions and the spectrum are known to show fractal structures. Such wavefunctions are termed critical. We present a phase diagram of the energy spectrum for varying the nonlinearity. It consists of three portions: a forbidden region, the spectrum of critical states and the spectrum of stationary solitons. We show that the energy spectrum of critical states remains intact, irrespective of the nonlinearity in the large number of stationary solitons.